Biophysical Journal
Volume 89
November 2005
3615–3627
3615
Probing Vesicle Dynamics in Single Hippocampal Synapses
Matthew Shtrahman,* Chuck Yeung,y David W. Nauen,z Guo-qiang Bi,z and Xiao-lun Wu*
*Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260; ySchool of Science,
The Pennsylvania State University at Erie, Erie, Pennsylvania 16563; and zDepartment of Neurobiology, University of Pittsburgh
School of Medicine, Pittsburgh, Pennsylvania 15261
ABSTRACT We use fluorescence correlation spectroscopy and fluorescence recovery after photobleaching to study vesicle
dynamics inside the synapses of cultured hippocampal neurons labeled with the fluorescent vesicle marker FM 1–43. These
studies show that when the cell is electrically at rest, only a small population of vesicles is mobile, taking seconds to traverse the
synapse. Applying the phosphatase inhibitor okadaic acid causes vesicles to diffuse freely, moving 30 times faster than vesicles
in control synapses. These results suggest that vesicles move sluggishly due to binding to elements of the synaptic cytomatrix
and that this binding is altered by phosphorylation. Motivated by these results, a model is constructed consisting of diffusing
vesicles that bind reversibly to the cytomatrix. This stick-and-diffuse model accounts for the fluorescence correlation spectroscopy and fluorescence recovery after photobleaching data, and also predicts the well-known exponential refilling of the readily
releasable pool. Our measurements suggest that the movement of vesicles to the active zone is the rate-limiting step in this
process.
INTRODUCTION
Most neurons communicate via chemical synapses. In this
process, vesicles in the axon termini (boutons) of the presynaptic cell dock at the active zone and undergo exocytosis in
response to action potential triggered Ca21 influx, emptying
neurotransmitter into the synaptic cleft. The bouton replenishes lost vesicles by recycling portions of the plasma membrane to create new vesicles via endocytosis. In the 1990s,
Betz and colleagues (1) developed the fluorescent marker
FM 1–43 that labels recycling vesicles. By imaging dye accumulation or depletion at the synapse, one can study vesicle
recycling and exocytosis in a variety of preparations including central synapses (2–4). Together with electrophysiological studies, these experiments provide strong evidence that
synaptic vesicles are divided into distinct functional pools.
These include a readily releasable pool (RRP) that stains
with FM 1–43 and is likely docked and a reserve pool (RP)
that is also labeled but is twice as large (4) and is remote from
the active zone (5–7). Interestingly, the majority of vesicles
in these synapses do not become labeled at saturating levels
of fluorescent staining, and thus do not participate in recycling; these vesicles comprise the resting pool. Electrophysiological studies show that stimulation at even moderate
frequencies (10 Hz) (8) depletes the RRP faster than the RP
can replenish it (9–11). Thus, the dynamics of RP vesicles
influence the efficacy of synaptic transmission.
Several studies suggest that vesicles are associated with a
variety of structural proteins (cytomatrix) within the synapse
and with motor proteins (12–17). Much of this work has
focused on the synapsin family of phosphoproteins, which
tethers vesicles to actin filaments (18–20). In response to
Ca21 entry, these proteins become phosphorylated and
Submitted January 7, 2005, and accepted for publication August 9, 2005.
release vesicles (21,22), making these vesicles available to
join the RRP.
Despite these observations, a physical picture of how RP
vesicles move to the active zone is still lacking, particularly
in central synapses. For example, recovery of the RRP, known
as ‘‘refilling’’, is also observed in the absence of Ca21 influx
(23) when vesicle fusion is stimulated with the application
of hypertonic sucrose solution (8,9,12,24–26). This Ca21independent refilling displays a similar exponential recovery
to that observed in response to membrane depolarization
(8,9,27). Traditionally, this empirical observation is thought
to reflect the mobilization of RP vesicles to the active zone
(23). However, previous studies in these and other synapses
containing synapsin find no measurable vesicle motion in
either resting or electrically stimulated synapses (28,29).
Moreover, Pyle and co-workers provide evidence that refilling is due to the rapid endocytosis of docked vesicles
commonly known as ‘‘kiss and run’’ (24), rather than vesicle
movement. Also, recent measurements by Deak et al. (30)
demonstrate that synaptobrevin-2 is critical for rapid endocytosis and that removing this protein slows refilling by a
factor of three. Together, these findings cast doubt on the role
of vesicle movement in refilling. In addition, the RRP recovers even more slowly after sustained exocytosis compared
to the faster refilling described above (10,31). The mechanism
for this form of synaptic depression is unknown, although
vesicle motion has been implicated (24). Lastly, the role of
actin in vesicle mobility in these synapses has recently come
into question (32). Thus, it remains unclear how RP vesicles
move to the active zone and how this process is regulated.
Studying vesicle dynamics in most central synapses is
challenging primarily due to bouton size. These small (;0.1
mm3) boutons are packed with hundreds of synaptic vesicles
that are ;40 nm in diameter, which is well below the
Address reprint requests to X. L. Wu, E-mail: xlwu@pitt.edu.
2005 by the Biophysical Society
0006-3495/05/11/3615/13 $2.00
doi: 10.1529/biophysj.105.059295
3616
diffraction limit of visible light. Therefore, imaging synaptic
vesicles directly using light microscopy (33) is problematic.
Here we report the use of fluorescence correlation spectroscopy (FCS) (34) to study vesicle dynamics in small central
synapses for the first time by recording the fluorescence intensity fluctuations of FM 1–43 labeled synaptic vesicles in
cultured hippocampal neurons. These fluctuations reflect the
movement of vesicles in and out of a diffraction-limited laser
spot (Gaussian radius w ¼ 0.11 mm). Together with fluorescence recovery after photobleaching (FRAP) (35), our results
indicate that there exists a small fraction (;27%) of mobile
vesicles that exhibit slow restricted motion within an immobile vesicle cluster. This motion is sped up ;30-fold after
applying the phosphatase inhibitor okadaic acid (OA),
suggesting that the vesicles’ sluggish dynamics are due to
phosphorylation-regulated binding within the bouton. To
explain these data, a model consisting of a pool of diffusing
vesicles that reversibly stick to and release from the cytomatrix is constructed. This simple model agrees well with
both the FCS and FRAP data, and it also reproduces the previously observed exponential refilling of the RRP.
MATERIALS AND METHODS
Primary cell culture
Cultures of dissociated embryonic rat hippocampal neurons were prepared
as described previously (36). Cells were used for experiments after 12–18
days in culture.
Fluorescence labeling
The culture was constantly perfused with room (;23C) or low (14–16C)
temperature HEPES-buffered saline (HBS) solution containing the following (in mM): NaCl 150, KCl 3, CaCl2 3, MgCl2 2, HEPES 10, glucose 5, and
pH 7.3 for all experiments unless stated otherwise. Synapses were loaded
with dye by perfusing cells with HBS containing 10–15 mM FM 1–43
(Synaptogreen, Biotium, Hayward, CA) and 50–90 mM KCl for 60 s,
followed by perfusion with HBS containing only dye for 30 s. This was
followed by a fast perfusion of dye-free (typically Ca21-free) HBS for
10 min at a rate .2 ml/min. In some experiments, 300 mM ADVASEP-7
(Biotium) was added for 1 min to the dye-free HBS, beginning 1 min after
the initiation of the fast perfusion (37). The majority of images of FM 1–43
puncta were taken with a charge-coupled device (CCD) camera (Hamamatsu
C9100-12, Hamamatsu City, Japan), using the same microscope and fluorescent filters as described for FCS below.
Fixation
Synapses used in experiments with fixed cells were loaded with AM 1–43
(Biotium) using a similar protocol to the one described above. Cells were
then placed in 4% paraformaldehyde for 30 min, followed by rinsing several
times in phosphate-buffered saline (PBS). Cells were stored in PBS up to the
time of the experiment.
FCS measurements
Fluorescence correlation spectroscopy (FCS) was used to investigate the
vesicle dynamics of the recycling pool. The experiments were carried out on
Biophysical Journal 89(5) 3615–3627
Shtrahman et al.
an inverted microscope (Nikon TE300, Melville, NY), using a 1003 1.3
numerical aperture oil immersion lens. Light from a Xenon arc lamp was
projected into the back port through a Nikon fluorescence attachment (Nikon
TE-FM), an excitation filter (Chroma D470/40, Rockingham, VT),
a converging lens (f ¼ 30 cm), and a 50/50 beam splitter. The other input
to the beam splitter consisted of two aligned parallel laser beams. An argon
laser beam (l ¼ 488 nm) was used as the excitation beam and was focused
by the microscope objective to a diffraction-limited spot. A HeNe (l ¼ 632
nm) laser beam was used to mark the position of the excitation spot, which
does not exit the filter cube (Chroma HQ510LP, Q497LP). The FM 1–43
labeled puncta were visualized under epifluorescence and positioned onto
the HeNe spot by a manual or a motorized microscope stage (SD
Instruments, Grants Pass, OR). Measurements were performed with all
light sources blocked except for the excitation laser (;0.5 mW). A confocal
geometry was used in which the fluorescence intensity I(t) from the synapse
was imaged onto a 50 mm pinhole placed in the side port and was measured
using an avalanche photodiode (APD) (EG & G SPCM-100, Wellesley,
MA) and an autocorrelator (ALV-5000, Langen, Germany). The pinhole, the
collection optics, and the excitation spot define the Gaussian detection
2
2
volume or the ‘‘light box’’ (er =2w ) with a radius w ¼ 0.11 mm, calibrated
by performing FCS on dyes with a known diffusion coefficient. This radius
is consistent with the size of the confocal detection volume measured by
scanning subresolution (40 nm) fluorescent beads (Fig. 1) and represents the
distance that a freely diffusing object must traverse for the correlation
function to decrease by 50% (38). The raw fluorescence intensity I(t) was
typically binned to 10 ms and then fit to an exponential curve IB(t) ¼
I0exp(t/tB), which accounts for the photobleaching (typically tB . 200 s).
The fluorescence intensity-intensity autocorrelation function G(t) ¼
ÆdI(t)dI(t 1 t)æ/ÆI(t)æ2 was calculated, where dI(t) ¼ I(t) IB(t) and Æ. . .æ
represents a time average.
FRAP measurements
FRAP measurements were made using the same experimental setup as
described above for FCS with slight modification. The intensity of the
excitation beam was increased to ;100 mW for ;0.5 s to bleach the synapse
by moving a neutral density filter out of the light path using a solenoid
actuator. This bleaching was moderate, reducing the intensity in the light
box to 35.40% 6 0.05% of its original value. Camera images of bleached
synapses showed a decrease in the total synaptic fluorescence of 13% 6 2%.
The estimated size of the mobile pool was adjusted to reflect this loss.
During the bleaching the APD was blocked to avoid saturation and damage.
The APD was unblocked within ;100 ms of the completion of the bleaching.
The autocorrelator recorded the intensity throughout the experiment. The
intensity before bleaching Ipre was average for 5 s. At t ¼ 0 the bleaching
was completed, the APD was unblocked, and the fluorescence intensity I(t)
was recorded. The fraction of fluorescence recovery was calculated as R(t) ¼
[I(t) I(0)]/[Ipre I(0)].
For the fluctuation analysis of the FRAP experiments, the fluorescence
intensity after bleaching I(t) was fit to an exponential recovery IR(t) ¼ I1 I0exp(t/tR). Similar to FCS experiments, the fluorescence intensityintensity autocorrelation function G(t) ¼ ÆdI(t)dI(t 1 t)æ/ÆI(t)æ2 was
calculated, where dI(t) ¼ I(t) IR(t).
Application of OA
A total of 2 mM OA (LC Laboratories, Woburn, MA), diluted from frozen
stock solutions aliquoted in dimethylsulfoxide (DMSO), was added after dye
loading such that the final concentration of dimethylsulfoxide did not exceed
0.1%. For experiments using OA, regions of interest (ROIs) were drawn around
synapses that appear as fluorescent puncta, as well as neuronal processes
labeled nonspecifically. Normally, nonspecific labeling is estimated by
measuring the fluorescence remaining in puncta after exhaustive exocytosis.
Since electrically stimulated exocytosis may be altered by OA, nonspecific
Probing Vesicle Dynamics
3617
FIGURE 1 FCS measures vesicle dynamics in
single synapses. (A) A schematic of the FCS detection
volume (light box) is shown overlying a typical large
synapse labeled with FM 1–43 (scale bar 0.5 mm).
(B) A plot of the normalized intensity measured by
scanning the detection volume along the long (n) and
the short (n) axes of this synapse as well as along a 40
nm fluorescent bead (s). A plot of the Gaussian light
box I ¼ I0exp(r2/2w2) (solid line), where w ¼ 0.11
mm, is also shown. (C) The intensity trace measured
from a single synapse is fit to an exponential function
(shaded trace) and is used to calculate the autocorrelation function G(t) shown in (D) (see Materials and
Methods).
labeling in regions of neuronal processes devoid of puncta was used to estimate the nonvesicular contribution to the synapses’ fluorescence before and
after adding OA. A decrease in background fluorescence was observed upon
adding OA. This secondary effect is small but cannot be explained entirely
by photobleaching. If one assumes that the decrease in background intensity
is uniform, then the fraction of dye lost to this secondary effect is ,10% of
the puncta’s initial fluorescence. The fading in puncta greatly exceeded this
change in background and is not due to exocytosis (39) (Appendix A). The
difference between fading in the synapses and fading in the background was
attributed to the dispersion of vesicles.
Synapse size
We measured synapse size by scanning individual puncta via scanning stage
confocal microscopy as shown in Fig. 1 B. However, this process is rather
slow. To gather sufficient statistics, the synapse area was measured by plotting the intensity along the long and short axes of camera images of fluorescent puncta. The baseline intensity was subtracted from each intensity
profile and the full width half maximum (FWHM) was calculated. The
intensity profile was approximated as a Gaussian function, allowing the
FWHM to be converted to a Gaussian radius, wI. This image intensity profile
represents the actual synapse shape profile convolved by the point spread
function (PSF) of the microscope (see Appendix B, Fig. 9 B). If all three
profiles are assumed to be Gaussian, than the radius ws along a given axis s of
the synapse can be estimated as w2s ¼ w2I w2PSF ; where wPSF is the Gaussian
radius of the PSF. The synapse and light box area were calculated by
approximating the synapse as an ellipse of area A ¼ pwshort wlong and the
light box as a circle of area A ¼ pw2 :
Synaptic motion
Synaptic boutons are dynamic structures whose shape and size evolve with
time (40). Such synaptic motion could contribute to the measurement of
fluorescence intensity fluctuations and fluorescence recovery if the fluorescent synapse moves relative to the fixed laser beam. To determine the contribution of this motion, we used video fluorescence microscopy to record the
center of mass position of individual synapses labeled with FM 1–43 (see
Fig. 3 A). The video rate was three frames per second. This measurement
was compared to the intrinsic drift of the experimental setup by recording the position as a function of time of 0.42 mm diameter fluorescein
isothiocyanate-labeled beads adsorbed onto a glass coverslip. Puncta and
beads were identified manually, and the center of mass position ~
rcm ¼
+i Ii~
ri = +i Ii for each 1 3 1 mm2 ROI containing a punctum was calculated
for each frame, where Ii and ~
ri are the fluorescence intensity and position,
~2 ðtÞæ was calculated
respectively, of the ith pixel in the ROI. The average ÆDr
for 30 synapses and is plotted versus t (see Fig. 3 B). The slope of this line is
equal to 4DCM, where the effective diffusion coefficient of the center of mass
is DCM ¼ 5.4 3 1015 cm2/s. As will be shown below, this diffusion coefficient is about three orders of magnitude smaller than the vesicle dynamics
measured by FCS or FRAP.
All errors and error bars represent the mean 6 SE, unless stated
otherwise.
RESULTS
FCS measures sluggish vesicle dynamics
A typical synaptic vesicle FCS measurement is depicted in
Fig. 1. Here the laser spot and detection volume (light box) is
positioned onto a synaptic bouton labeled with FM 1–43
(Fig. 1 A). It is important that vesicles can leave the light box
for fluorescence intensity fluctuations to be observed. The
lateral dimensions of this typical large synaptic bouton are
measured by scanning the detection volume across the
synapse, which are displayed in Fig. 1 B. The narrow lateral
Biophysical Journal 89(5) 3615–3627
3618
dimension of the bouton is less than twice the width of the
light box. In addition, the height of the synapse is comparable to the narrow lateral dimension, whereas the height of the
light box is 3–5 times larger than its width (41). Thus, motion
perpendicular to the coverslip is not detected (42). This
natural confinement can be taken into account, and the vesicles can be treated as if they are moving in a constrained two
dimensional system (42). The area of an ensemble of labeled
synapses was measured from camera images resulting in an
average area of 0.34 6 0.02 mm2 (n ¼ 33). This area is 9 6 2
times larger than the area of the light box (0.038 6 0.009
mm2) and is consistent with the average cross sectional area
of ;0.3 mm2 measured from electron micrographs of
cultured hippocampal synaptic boutons (5). The ratio of
synapse to light box size is also consistent with photometric
measurements that show that the total amount of fluorescence emanating from these synapses is an order of magnitude larger than the fluorescence measured in a typical FCS
measurement (Appendix B). In the FCS measurements, we
also took advantage of the great heterogeneity in bouton
sizes (43) by selecting large boutons such as the one shown
in Fig. 1. These boutons are similar in size to those displayed
as examples of normal architecture in several electron microscopy studies (5,7,44). Hence, the light box is small
enough that vesicles can exit this volume, which is required
for observing fluorescence fluctuations.
Fig. 1 C displays the fluorescence intensity from a single
synapse as a function of time. Here the number of photons
measured during each time bin decays at a modest rate due to
photobleaching and can be corrected after fitting to an exponential function (see Materials and Methods). In addition
to the overall decay of the time trace, one observes intensity
fluctuations resulting from putative vesicle motion. The fluorescence intensity autocorrelation function G(t) calculated
from this time trace is shown in Fig. 1 D. Here, G(t) quantifies the correlation between pairs of fluorescence intensity
fluctuations observed a time t apart. As vesicles redistribute,
these correlations decay, providing information about the
underlying dynamics.
Shtrahman et al.
These measurements were repeated for an ensemble of
labeled synapses (n ¼ 39), each with an integration time
of T ¼ 200 s. As shown in Fig. 2 A, there is a great deal of
heterogeneity within the ensemble, particularly in the
amplitude of the correlation function G(0) (coefficient of
variation cG(0) ¼ 0.92). This large variation is not surprising
and has been observed in several other measurements in
these synapses, such as synapse size and release probability
(8,43,45). These factors along with the variation in the arrangement and the number of vesicle clusters may contribute
to the heterogeneity in the observed dynamics. For a subset
of these synapses (n ¼ 23), the FCS measurement was repeated at a different location (at least one light box diameter
away) within the same synapse. We find that the variation in
G(0) within the synapse is ;½ of that between synapses,
indicating that about one-half of the heterogeneity is intrinsic
to the population of synapses. The correlation between measurements within the same synapse is demonstrated in Fig. 2
C. To examine the average behavior of vesicles in these synapses, the autocorrelation functions from individual boutons
were averaged (Fig. 2 B). The amplitudes of these fluctuations are orders of magnitude greater than those measured in
the synapses of fixed cells, demonstrating that the fluctuations are inherent to the living synapses.
The correlation time is one important parameter that can
be extracted from the autocorrelation function. Our experiment yields a correlation time of t ½ ¼ 2.8 6 0.4 s, where
G(t ½) ¼ ½G(0). We can gain physical intuition about this
number by relating it to a diffusion coefficient and an effective viscosity of the vesicles’ surroundings. If we assume that
t ½ corresponds to a diffusion time t ½ ¼ w2/D, then we find
an effective diffusion coefficient of D ¼ 4.3 6 0.7 3 1011
cm2/s. This diffusion constant is ;8000 times larger than
that measured for synaptic motion using video fluorescence
microscopy (Fig. 3 and Materials and Methods). Thus, the
observed FCS fluctuations cannot be attributed to any relative motion between the synapse and the laser spot. Assuming
that the vesicles diffuse in a medium characterized by a
single viscosity coefficient, the Stokes-Einstein relation
FIGURE 2 Synapses are heterogeneous. (A) Ensemble of G(t)’s measured from 39 different synapses. (B)
The average of the correlation functions
in A is plotted (d) with the amplitude
G(0) ¼ 0.016 6 0.002 and the
correlation time t½ ¼ 2.82 6 0.4 s
marked. The green line represents the fit
to the stick-and-diffuse model (tB ¼ 4.5
6 1.1 s, tU ¼ 2.1 6 1.5 s, tD ¼ 0.19 6
0.17 s). The blue line with error bars represents the average correlation function for low temperature (14–16C) exposed synapses (t½ ¼ 10.5 6 0.3 s, n ¼ 16).
The solid squares represent the average correlation function for synapses labeled with dye and fixed with paraformaldehyde (n ¼ 41). For both the control and
the fixed synapses, the error bars (mean 6 SE) are the same size or smaller than the points. (C) The spatial heterogeneity was measured by making two FCS
measurements spaced at least one light box diameter away within the same synapse (n ¼ 23). The G(0) of the first measurement is plotted against G(0) of the
N
2 1=2
second measurement and scatter about the line of slope one. The intrasynaptic heterogeneity ðð1=NÞ +j¼1 ðGð0Þ2nd
Gð0Þ1st
is 58% of the intersynaptic
j
j Þ Þ
N
1st 2 1=2
heterogeneity ððN!=ðN 2Þ!2!Þ +j¼1 +k,j ðGð0Þ1st
Gð0Þ
Þ
Þ
:
j
k
Biophysical Journal 89(5) 3615–3627
Probing Vesicle Dynamics
FIGURE 3 Synapse center of mass motion does not contribute to the FCS
measurement. (A) The inset displays the trajectory ~ðtÞof
r
the center of mass
of a typical synapse (0.3 s/step, totaling RT ¼ 90 s, scale 5 nm). The mean
T
2
~ðtÞ2 æ ¼ ð1=TÞ 0 ½ðr
~ðt91tÞ ~ðt9Þ
squared displacement ÆDr
r
dt9 calculated
from this synapse’s trajectory is plotted below the inset. (B) The average
~ðtÞ2 æ was calculated for 30 synapses and is displayed (top line with error
ÆDr
~ðtÞ2 =tæ ¼ 4DCM ¼ 2.15
bars) along with a linear fit (shaded line) of slope ÆDr
2
~ðtÞ2 æ for 0.42 mm
nm /s. The average mean-square displacement ÆDr
fluorescent beads (bottom solid line, with the thickness exceeding the error,
n ¼ 75) adsorbed to a glass coverslip is displayed along with a linear fit
(shaded line) of slope 4DCM ¼ 0.22 nm2/s.
(D ¼ kB T=6pah) yields an effective viscosity h ¼ 25 poises
for T ¼ 293 K for the vesicle radius a ¼ 20 nm. This
viscosity is 2,500 times larger than water and ;100 times
larger than expected for inert particles of this size diffusing in
the cell (46). Accordingly, one of the goals of this work is to
understand the source of this large correlation time and to
develop a model of the vesicle motion that will help us
understand the observed dynamics.
To further probe vesicle dynamics we also examined the
temperature dependence of vesicle motion (47). Increasing
3619
the temperature to near physiological temperatures increases
the rate of spontaneous exocytosis and thus the depletion of
FM 1–43 from the puncta. This severely restricts the time
available for performing time averaging techniques such as
FCS, particularly when an ensemble of synapses is required
to collect statistics. Instead, we examined the effect of lowering the temperature (14–16C) on vesicle dynamics. Not
only was the fluorescence in these lower temperature puncta
more stable, but the vesicle dynamics measured in these
synapses were significantly slower (t ½ ¼ 10.5 6 0.3 s) than
those in control synapses measured at room temperature
(t ½ ¼ 2.82 6 0.4 s) (Fig. 2 B). This temperature dependence
offers further confirmation that we are observing physiological vesicle motion.
Recycling vesicles consist of a mobile and an
immobile pool
FRAP measures the mobility of fluorescent objects by
monitoring the fluorescence intensity as it recovers within an
area previously bleached by an intense laser beam (35). Compared to FCS, it is more suited for measuring slow dynamics
and can provide complementary information about mobility
and the fraction of mobile particles. The same FCS experimental setup as described above was used to measure FRAP
of FM 1–43 labeled vesicles within the synapse. Fig. 4 A
shows a labeled synapse before and ;1 min after a portion of
the synapse has been bleached. In addition, the same synapse
is displayed after application of high K1 bath solution. The
diminished fluorescence throughout the bouton, including
the bleached region, indicates that vesicles within the
FIGURE 4 FRAP resembles refilling of RRP. (A) A synapse labeled with FM 1–43 is shown before and ;1 min after an area is photobleached with a laser.
The same synapse is also shown after high K1 bath is applied. The images are displayed twice, emphasizing the high (H) and low (L) end of the gray scale
(scale bar 0.5 mm). (B) A sampling of FRAP curves (n ¼ 12) randomly chosen from the full ensemble (n ¼ 47). The normalized, ensemble-averaged correlation
function calculated from the fluctuations in the FRAP measurements (green trace) is plotted along with the corresponding correlation function from FCS
measurements (black trace) in the inset. (C) The average FRAP response of the entire ensemble is plotted with error bars (standard deviation) and is fit
to a double exponential (dotted line) A(f(1 exp(t/tF)) 1 (1 f(1 exp(t/tS))) with tS ¼ 4 s, tF ¼ 40 s, A ¼ 0.15, and f ¼ 0.58. Rescaled refilling data
(see Discussion) of the RRP measured by Morales et al. (12) (n, scaling factor 0.10) and Stevens and Wesseling (31) (n, scaling factor 0.16) reveal short and
long time refilling, respectively. The solid red line is the fit of the simplified stick-and-diffuse model to the fast refilling experiments with fitting parameters
tB ¼ 4.32 s and tU ¼ 0.59 s. The inset shows the same data on a semilog scale to emphasize early times.
Biophysical Journal 89(5) 3615–3627
3620
synapse are still able to undergo exocytosis and that the
synapse is still viable after photobleaching. In addition to the
traditional analysis of FRAP data described below, we also
calculated G(t) for the FRAP signal and compared it to G(t)
measured during FCS experiments where no photobleaching
had occurred. The inset to Fig. 4 B shows that the average
correlation function measured after photobleaching closely
resembles the average correlation function for control synapses. Hence, vesicle dynamics are not significantly altered
by photobleaching.
The recovery from an ensemble of synapses and the average recovery are displayed in Fig. 4, B and C, respectively.
Similar to the measurements of G(0), there is significant heterogeneity in the asymptotic level of fluorescence recovery
(coefficient of variation cR ¼ 0.35). The average recovery is
;15%, indicating that a vast majority of labeled vesicles are
not mobile and explaining why the bleached area in Fig. 4 A
remains dark (29). The fluorescence recovery has two identifiable timescales. The fast timescale t F 4 s agrees well
with the correlation time t ½ ¼ 2.8 6 0.4 s measured by
FCS. The slow timescale t S 40 s, which is comparable to
the total FCS integration time T, is not accessible in those
measurements.
The amplitude of the correlation function G(0) measured
by FCS is the variance of the number of labeled vesicles in
the light box. For the average correlation function displayed
in Fig. 2 B, G(0) ¼ 0.016 6 0.002. For freely diffusing
particles, the fluctuations of the number of particles in the
light box obey Poisson statistics with the result G(0) ¼ 1/ÆNæ,
where ÆNæ is the average number of fluorescently labeled particles in the light box. However, for a system containing an
immobile population, G(0) ¼ ÆNMæ/ÆNæ2 (48), where ÆNæ ¼
ÆNMæ 1 ÆNIæ 1 ÆNBæ and ÆNMæ and ÆNIæ are the average
number of mobile and immobile vesicles, respectively, in the
light box. ÆNBæ is the amount of background fluorescence in
units of vesicles. Measuring the fluorescence remaining in
puncta after sustained exocytosis gives ÆNBæ/ÆNæ ¼ 0.39 6
0.01 (Appendix B). Also, FRAP measurements performed
on unloaded puncta show no measurable fluorescence
recovery, indicating that the background fluorescence
fraction (ÆNBæ) does not contribute to the measured vesicle
dynamics. We can estimate the average number of vesicles in
our light box (ÆNIæ 1 ÆNMæ ¼ 0.61ÆNæ) by solving the above
expression for ÆNæ ¼ (ÆNMæ/ÆNæ)/G(0), where ÆNMæ/ÆNæ can
be measured by the asymptotic level of the FRAP curve in
Fig. 4 C. This level must be adjusted for the total synaptic
fluorescence remaining after bleaching, which is 87% 6 2%.
The remaining fluorescence recovers to 16.2% 6 0.9% on
the timescale of the FRAP experiment (;70 s), which is
comparable to the FCS integration time. Hence, G(0) reflects
only a fraction of this recovery, and the above ÆNMæ/ÆNæ is an
upper bound. (The FRAP signal recovers to ;10% in 10t ½
(;30s), which perhaps is a more appropriate value to compare with G(0) but is not rigorous. This value is consistent
with the scaling factor for fast refilling considered in the
Biophysical Journal 89(5) 3615–3627
Shtrahman et al.
Discussion.) This yields ÆNIæ 1 ÆNMæ , 6.0 6 0.4 labeled
vesicles in the light box and , 54 6 15 total labeled vesicles
in a typical synapse. This is consistent with the majority of
studies involving quantal dye uptake (4,6) and counting of
labeled vesicles with electron microscopy via photoconversion (7), which show that the total number of labeled vesicles
in the average synapse is 25–30, with one study measuring as
many as 120 (49). This result confirms that our earlier estimate of the ratio of the synapse to light box area is reasonable. More importantly, it demonstrates that both G(0)
and the asymptotic level of FRAP are small because there
exists a large population of immobile recycling vesicles, with
ÆNIæ/(ÆNIæ 1 ÆNMæ) ¼ 73% 6 2% on the timescale of
minutes.
Phosphorylation frees vesicles
The phosphatase inhibitor OA has been shown to increase
the mobility of synaptic vesicles at the neuromuscular junction (28,50), although this phenomenon may not be universal
among different synapse types (39). It is thought that this
occurs primarily by shifting the population of synapsin proteins to the phosphorylated state, which releases vesicles from
the synaptic cytoskeleton (18,20,51). Other studies such as
those by Sankaranarayanan et al. (32) suggest that vesicles in
hippocampal synapses bind to other structural proteins rather
than actin. Therefore, the stickiness of the synaptic cytoskeleton or other structural proteins may explain the observed
slow dynamics of these vesicles.
To explore this idea, we examined the effect of OA on
hippocampal synapses labeled with FM 1–43. Images show
that OA tends to fade and smear the majority (;90%) of
puncta, with the average punctum losing .70% of its vesicles
(Fig. 5 A). This large value indicates that the application of
OA frees vesicles that were previously immobile. We also
used FCS to measure the effect of OA on the dynamics of
these vesicles. The measurements show that these puncta can
be divided into two distinct groups, sensitive and resistant,
based on their correlation time (Fig. 5 B). Resistant puncta
are 50% brighter and exhibit dynamics whose decay time is
too long for the average correlation function to converge.
Similar effects of OA treatment were observed by Betz et al.
(50) in the neuromuscular junction. In contrast, sensitive
puncta are dimmer and exhibit dynamics whose average
decay time is t ½ ¼ 0.10 6 0.04 s, which is ;30 times faster
than the control synapses. The average correlation function
changes its form significantly and can be described well by
free diffusion in a confined geometry (Fig. 5 B). These dynamics agree reasonably well with the diffusion time measured for inert particles of this size in cells (46) as well as
synaptic vesicles in ribbon type synapses that lack synapsin
(52,53). Thus, eliminating the phophorylation-dependent
binding of RP vesicles to the cytomatrix allows them to
diffuse freely.
Probing Vesicle Dynamics
3621
FIGURE 5 OA frees vesicles. (A)
Fluorescence image of FM 1–43 labeled synapses before and 15 min after
continuous application of 2 mM OA
(scale bar 5 mm). By measuring the
labeling of neuronal processes, one can
estimate the nonspecific contribution to
the puncta’s fluorescence (see Materials
and Methods). The remaining intensity
is due to vesicles (;80%); .70% of
this vesicular fluorescence is lost to
diffusion after 15 min in OA. (B) The
average autocorrelation function from OA-sensitive synapses (n ¼ 7) is plotted (solid line) along with a fit (shaded line) to two-dimensional (2D) free diffusion
with one dimension confined to twice the light box size (42). The cumulative histogram displayed in the inset shows that synapses can be divided into two
groups, sensitive (n) and resistant (s), based on their correlation times. Note that a log scale is used to display the widely separated correlation times.
DISCUSSION
Our experiments suggest that the motion of synaptic vesicles
can be measured with FRAP and FCS in cultured hippocampal neurons at the level of single synaptic boutons despite
their small size. The small G(0) measured by FCS and the
slight asymptotic recovery measured independently by FRAP
are both consistent with the picture that a large fraction of
recycling vesicles are immobile. Together these quantitative
measurements provide an estimate for the number of labeled
vesicles in the light box and the synapse, which agrees with
previous measurements using fluorescent and electron microscopy in these synapses (4,6,7,49). Also, results from both
techniques indicate that mobile vesicles take on the order
of seconds or longer to move across the bouton. Control
FCS experiments performed on labeled vesicles in synapses
of fixed cells indicate that this motion is intrinsic to living
synapses and that the FCS signal in live synapses is not due
to fluctuations in laser intensity or other instrument noise.
Further, vesicle dynamics in synapses is about three orders of
magnitude faster than synaptic motion and mechanical drift
measured by video fluorescence microscopy. Finally, the
timescale of vesicle dynamics and its temperature dependence agrees with the time required to refill the RRP,
which we discuss in detail below. These facts strongly imply
that we are indeed measuring the dynamics of synaptic
vesicles.
an apparent diffusion coefficient that is 30 times larger than
control synapses. Lastly, we compared the experimental
correlation function to the correlation function predicted for
one and two dimensional diffusion, as well as for free diffusion in confined geometries (42). In all cases the fits were
marginal (see Appendix C, Fig. 11). Hence, phosphorylationdependent vesicle binding to the synaptic cytomatrix is likely
the source of the sluggish dynamics, and normal vesicle motion is not simply free diffusion.
Motivated by our experimental results and the of body of
work on synapsin (18–20), we constructed a model of diffusing vesicles that stochastically bind to and release from
the synaptic cytomatrix via a Poisson process (Fig. 6). When
the vesicles are unbound, they are free to diffuse with a
diffusion constant, D, so that the characteristic diffusion time
over the light box is t D ¼ w2/D. In the free state, vesicles
Vesicles exhibit stick-and-diffuse dynamics
Several results lead us to believe that the observed slow vesicle motion is not free diffusion. First, the effective diffusion
coefficient for vesicle motion is ;100 times smaller than that
measured for inert particles of the same size diffusing in cells
(46). Next, we observe that the effective diffusion constant
changes by a factor of ;4 when the temperature is lowered
by ;8C. In contrast, the Stokes-Einstein relationship for
ideal diffusion predicts only a 3% change for the same decrease in temperature. Also, the motion of synaptic vesicles
is altered significantly by the application of the phosphatase
inhibitor OA, which results in vesicles diffusing freely with
FIGURE 6 Refilling of the RRP is modeled by stick-and-diffuse
dynamics. A schematic of the stick-and-diffuse model depicts mobile
vesicles stochastically alternating between a bound and a free state. Bound
vesicles become free at a rate t1
B ; the inverse of the average time they
remain stuck. Free vesicles diffuse with a diffusion coefficient D and become
stuck at a rate t1
U : In addition to mobile vesicles that undergo stick-anddiffuse dynamics, there exists an immobile pool of vesicles, which remains
bound on timescales much longer than the transient binding times of the
mobile pool. Refilling of the RRP can be modeled by including docking sites
that act as perfect sinks.
Biophysical Journal 89(5) 3615–3627
3622
become bound at a rate 1/t U. Once bound, the vesicles
become free again with an unbinding rate 1/t B. Therefore,
the unbound and bound states last for average times t U and
t B, respectively. The correlation function for this model can
be expressed in terms of an infinite sum, allowing G(t) to
be calculated numerically (Appendix C). Fig. 2 B shows that
the fit of the stick-and-diffuse model to the FCS data is quite
good, with the fitting parameters t B ¼ 4.5 6 1.1 s, t U ¼ 2.1
6 1.5 s, and t D ¼ 0.19 6 0.17 s.
Therefore, our picture of vesicle dynamics is as follows.
The majority of recycling vesicles are immobile, and even
mobile vesicles spend ;70% (t B/(t U 1 t B)) of their time
bound. When bound, these vesicles remain stuck for an
average time of ;5 s. Once unbound, the vesicles are free to
move about the bouton, becoming bound again after an
average time of ;2 s. Since t U/t D 10, the vesicles can visit
an area much larger than the light box while free. Note that
the fit of the model to the experimental autocorrelation
function is sensitive to t U and t B but insensitive to t D as long
as t D t U. Despite the large uncertainty in t D, the free
diffusion time obtained in our fits is consistent with the
diffusion time measured in the presence of OA (t ½ ¼ 0.10 6
0.04 s).
Although mobile vesicles spend a majority of their time
bound, it is important to make a distinction between mobile
vesicles that bind transiently and vesicles that reside in the
immobile pool. Since the sticking time t B is much smaller
than the integration time, these mobile vesicles contribute to
both G(0) and to the amount of fluorescent recovery after
photobleaching. In contrast, the immobile pool vesicles remain bound on timescales on the order of, or larger than, the
duration of the FCS and FRAP experiments. Thus, the immobile pool is a long-lived state compared to the transient binding of the mobile vesicles, and the small G(0) and incomplete
fluorescence recovery can only be explained by the existence
of two distinct vesicle populations. A population of immobile
vesicles has been observed in these (29) and in other synapses
(28,54) and may be characteristic of many synapses.
Mobilization of vesicles is the rate-limiting step
for refilling the RRP
Refilling experiments monitor the recovery of exocytosis
after the entire RRP of vesicles has fused. Although other
mechanisms have been proposed (24), this phenomenological observation is thought to reflect the mobilization of RP
vesicles to the active zone (23). However, this had not
previously been addressed by direct measurements of vesicle
mobility. The majority of studies show that the refilling
process can be fit by a single exponential with a relaxation
time of 3–10 s. This agrees with the typical correlation time
t ½ ¼ 2.8 s and the fast fluorescence recovery time t F 4 s
measured in our experiments. This agreement suggests that
vesicle movement to the active zone might be the ratelimiting step in refilling. If this is true, then this movement
Biophysical Journal 89(5) 3615–3627
Shtrahman et al.
alone should be able to explain the exponential recovery.
Fig. 4 C shows refilling data measured by Morales et al.
(2000) that has been rescaled to overlie the averaged data
from the FRAP experiments. We see that the refilling of the
RRP follows an identical time course as the fast (t F)
recovery of fluorescent vesicles into the light box. Next we
asked if the fast FRAP and refilling data could be explained
by the stick-and-diffuse dynamics used to model the FCS
experiments. To simplify the analysis we set t D ¼ 0, since
the diffusion time is an order of magnitude faster than the
other timescales. At t ¼ 0, a fraction F ¼ t U/(t U 1 t B) of
mobile vesicles are free. Additional vesicles continue to
unbind in an average time t B. Once free the vesicles diffuse
and, because t D ¼ 0, distribute instantaneously with uniform
probability throughout the synapse. Hence the time for
refilling the light box or the active zone, approximated as
a perfect sink (4), is determined solely by t B and has the form
(1 F 3 exp(t/t B)). The fit of the simplified stick-anddiffuse model to the refilling data is shown in Fig. 4 C. A
separate fit for the FRAP experiment was not done since the
refilling and FRAP data coincide. Despite the simplicity of
the model, the parameters optimized to fit the refilling and
FRAP experiments (t B ¼ 4.32 s, t U ¼ 0.59 s) agree
reasonably well with those optimized independently to fit the
FCS measurements (t B ¼ 4.5 6 1.1 s, t U ¼ 2.1 6 1.5 s). The
stick-and-diffuse model of synaptic vesicle dynamics is
consistent with both FCS and FRAP results, as well as the
previously observed refilling of the RRP. These results,
however, do not rule out other mechanisms of refilling such
as rapid endocytosis (24).
In contrast to the fast refilling described above, the RRP
recovers more slowly after extensive exocytosis (10,11,31).
The mechanism of this form of synaptic depression is unknown although several mechanisms, including vesicle
mobilization, have been suggested (24). In addition to fast
refilling, Fig. 4 C also shows rescaled data measured by
Stevens and Wesseling (31) for the refilling of the RRP after
depression was induced with 150 action potentials at 9 Hz.
The slow component (t S) of the FRAP signal matches the
slow recovery of the RRP after the sustained activity. (Experiments that measure both the fast and slow component of
refilling simultaneously (31) also fit the average FRAP data
well (data not shown).) Therefore, the slow recovery of the
RRP is consistent with the mobilization of vesicles. One
possible mechanism for the slow synaptic depression is that
after extensive exocytosis the rate of refilling of the RRP
is limited by the rate at which immobile vesicles join the
mobile pool. The slow refilling is not seen in the traditional
refilling experiments because the brief application of hypertonic solution only depletes the RRP. In contrast, sustained
electrical activity depletes both the RRP and the mobile pool
faster than they can be replenished by the immobile pool,
resulting in depletion, but with slower recovery. Hence, the
slow timescale for refilling appears only after both the docked
and the mobile pools undergo exocytosis. In contrast, our
Probing Vesicle Dynamics
experiments do not rely on exocytosis, allowing us to observe
vesicle mobilization more directly. We conjecture that immobile vesicles become free at minimal levels in resting
synapses and that this process manifests as the slow (t S)
fluorescence recovery measured in our experiments. If the
limited availability of immobile vesicles is truly responsible
for the slow recovery of the RRP, then this process is likely
to be a key regulatory point in the vesicle cycle (54). This
idea is consistent with experiments that show that OA frees
immobile vesicles, suggesting that the size of the immobile
pool is regulated by phosphorylation. Additional experiments
should address these issues.
APPENDIX A: APPLICATION OF OA DOES NOT
INCREASE EXOCYTOSIS
Previous work in other preparations has shown that application of OA
disrupts the synaptic vesicle cluster, with no evidence of increased
exocytosis reported (39,50). To confirm that OA does not result in the
release of dye via exocytosis, we monitored postsynaptic currents in our
culture preparation in the presence of OA. Fig. 7 shows current traces
recorded under voltage clamp from a single cell within a densely connected
network. Under normal conditions (Fig. 7 A), postsynaptic currents are
infrequent. No discernable change is observed when 2 mM or greater OA is
added to the extracellular bath (Fig. 7 B). In contrast, perfusing the culture in
high K1 solution results in numerous postsynaptic responses (Fig. 7 C).
Identical behavior was observed in all experiments (n ¼ 3). Thus, the loss of
fluorescence in FM 1–43 labeled puncta upon addition of OA is not due to
exocytosis.
3623
APPENDIX B: FCS DETECTION VOLUME IS A
SMALL PORTION OF THE SYNAPSE
The area of the light box is ;10 times smaller than that of the synapse,
suggesting that the FCS measurement observes a small fraction of the total
labeled vesicles in the synapse. To confirm this, we calibrated the mean
intensity measured by the avalanche photodiode (APD) during the FCS
experiment against the total fluorescence of FM 1–43 labeled puncta. This
time-averaged intensity measured by the APD should represent a small
fraction of the total fluorescence emanating from the labeled synapse. To
measure the total fluorescence intensity, synapses were loaded with FM 1–
43 using the same protocol as used in the FCS experiments. The FM 1–43
loaded synapses were illuminated with a Xenon arc lamp, and an image (Fig.
8 A) was taken with a camera using a specified gain and exposure time. The
synapses were unloaded by perfusing the coverslip three times with high K1
solution without dye, and a second image (Fig. 8 B) was taken using the
same settings. The two images were aligned, and a 1.0 mm circular ROI was
drawn around each punctum. The total intensity and the difference intensity
for each ROI was calculated (n ¼ 82 puncta). The histograms for both the
starting and difference (unloaded) intensities are displayed in Fig. 8, D and
E, respectively. The mean starting and difference intensities are 2.8 and 1.9
million counts per second, respectively. These values indicate that ;30% of
the puncta’s fluorescence is not released upon stimulation. A synapse-bysynapse analysis shows that 39% 6 1% of the puncta’s fluorescence remains,
and this value is used to estimate the nonspecific background labeling.
The intensities of these puncta measured by the camera in the front port
could then be calibrated against FCS intensities measured by the APD in the
side port of the microscope. This calibration actually involves calibrating
two sets of instruments: the APD and the laser used in the FCS experiment
against the lamp and the camera used in the above unloading experiment.
We describe these calibrations below.
First, we calibrated the 16-bit scale of the camera against the photons
counted by the APD. Since intensity is the number of photons per area per
FIGURE 7 Application of OA does not increase exocytosis. Twenty current traces recorded every 10 s from a single cell under voltage clamp in the presence
of (A) normal bath solution and (B) normal bath solution with 4 mM OA added. (C) High K1 bath solution. Note the different scale, demonstrating that
synapses in the network are release competent given the proper stimulus. Each experimental condition was presented sequentially from A to C. Within each
condition, blue traces were recorded earlier, red traces later. The top graph in each panel displays the traces superimposed on a 2D plot, whereas the bottom
graph shows each trace separated along the y axis.
Biophysical Journal 89(5) 3615–3627
3624
Shtrahman et al.
FIGURE 8 The total fluorescence of FM
1–43 labeled synapses. Image of a field of
FM 1–43 labeled puncta before (A) and
after (B) unloading with three rounds of
high K1 bath solution. (C) The difference
image of B subtracted from A. Identical
ROIs were drawn around puncta in A and B,
and the total intensity was calculated for
each ROI. (D) A histogram of the starting
intensities for three experiments is displayed in counts on the CCD camera per
second. (E) A histogram of the difference
intensities for the same experiments.
second, we must find the area over which the APD together with the pinhole
integrate the incoming photons under wide field illumination. Formally, the
pinhole in front of the APD convolves the image that the APD detects.
Similarly, we convolved the image that the camera detects with a window
function, W, to properly calibrate the intensities. To measure this window
function, we imaged subresolution 40 nm fluorescent beads illuminated with
the arc lamp. This image of subresolution beads reveals the PSF of the
optical system. The image of individual beads were projected into the side
port and scanned across the pinhole and APD at a known velocity (0.313
mm/s). Several of these line scans (Fig. 9 A) were averaged to give IAPD
(Fig. 9 C). Likewise, images of the beads from the same coverslip and with
the same illumination were imaged by the camera mounted in the front port.
Line scans along a single row of pixels though the middle of the beads
(Fig. 9 B) were averaged to give the PSF displayed in Fig. 9 C. Notice that in
Fig. 9 C the camera’s line scan along a row of pixels (PSF) is narrower than
the line scan measured by the APD. This is due to the fact that the camera is
measuring the PSF of the microscope, whereas the APD is measuring the
PSF convolved by some window function. To mimic the effect of the
pinhole, we convolve the line scan measured by the camera (PSF) with
a square window function W of various sizes d until it matches the line scan
measured by the APD (Fig. 9 C).
IAPD ðxÞ ¼
Z
Wðx x9ÞPSFðx9Þdx9;
where Wðx x9Þ ¼ 1 for jx x9j # d=2 and 0 otherwise. As the window
size increases, the convolved PSF spreads out and approaches the line scan
measured by the APD, with the best match being a window ;5.5 pixels or
440 nm measured in the object plane. When one applies the magnification of
the side port of 803, one finds a window of 35 mm. This agrees well with
physical size of the pinhole, which is 50 mm.
To calibrate the counts measured by the camera into photons measured by
the APD, we labeled a dendrite with FM 1–43 and illuminated it with the
same arc lamp as above. The dendrite’s image was both captured by the
camera (Fig. 10 A) in the front port and scanned across the pinhole and APD
in the side port (open squares Fig. 10 C). The position of the pinhole in
reference to the camera image is measured by illuminating the sample with
the laser spot, to which the pinhole has been aligned, and taking an image
with the camera (Fig. 10 B). A line scan in the x direction along the pixels of
the camera image was then convolved by a two dimensional 5.5 3 5.5 pixel
square window. This convolution integrates the intensity in the square
window as it moves along the image and is meant to mimic the pinhole being
scanned across the dendrite. The convolved line scan along the camera
image (solid squares) as well as the scan across the APD and pinhole (open
squares) are displayed in Fig. 10 C. After rescaling, the two curves collapse
onto each other, reaffirming the correct choice of the window function used
in the convolution. The result of the rescaling is that one photon measured by
the APD in the side port is equivalent to 39 counts measured by the camera
in the front port (on a 16-bit scale at the given camera settings). With
additional calculations, we find that our calibration agrees within a factor of
;2 of the manufacturer’s specifications.
Now we can express the total counts in the labeling experiment shown in
Fig. 8 in terms of photons collected by the APD per unit time. If we multiply
1/39 photons per count by the average total fluorescence emanating from the
synapse during 1 s, we can get the number of photons per second that the
FIGURE 9 Calculating the window
function. A total of 40 nm fluorescein
isothiocyanate-labeled beads were
sparsely adsorbed onto a glass coverslip
that was mounted onto a motorized
stage and were illuminated with an arc
lamp. (A) The intensity of individual
beads recorded by the APD as their
image is scanned across the pinhole. (B)
The intensity of individual beads from
the same sample plotted along a row of
pixels in the CCD image. (C) The average intensity profile measured by the APD in A (n) and by the camera in B (d) is plotted along with the average camera
profile convolved by a square window function of size 3 3 3 (n), 5.5 3 5.5 (h), and 7 3 7 ()) pixels.
Biophysical Journal 89(5) 3615–3627
Probing Vesicle Dynamics
3625
FIGURE 10 Counts on the CCD camera
calibrated in terms of counts on the APD.
(A) A schematic of a square window function being scanned across an image of
a dendrite labeled with FM 1–43 and illuminated with an arc lamp. The y coordinate
for the window function is given by the
position of the laser spot shown in B. (C)
This convolved intensity profile (n) is
scaled to the intensity profile measured by
the APD as the dendrite’s image is
physically scanned across the pinhole (h).
This scaling factor calibrates the counts on the 16-bit scale of the camera into photon counts measured by the APD. Notice that the two curves collapse onto
each other, indicating that the window function used in the convolution is accurate. The same dendrite is then illuminated with the laser spot, and the image is
scanned across the same pinhole and APD as above (s). This is scaled to best match the scan using the APD and arc lamp. This scaling factor provides the
calibration of the lamp intensity in terms of the laser intensity.
APD would measure with the same illumination. For the fully labeled
synapse this would be 72.2 3 103 photons/s.
The last step is to calibrate the different excitation sources, laser and xenon
arc lamps, used in the two experiments. To do this we scan the same dendrite
in the same location as above with a laser intensity typically used in the FCS
measurements (;0.005 mW) and measure the fluorescence intensity. This can
be directly compared to the analogous scan of the dendrite illuminated by the
arc lamp described above. Both are scanned in the same manner and measured
with the same APD and pinhole. The scan of the dendrite with the laser is
plotted (open circles) in Fig. 10 C. Notice that the profile of the dendrite is
narrower when excited with the laser than with the lamp. This improved
resolution is a well-known effect in laser confocal microscopy. The
fluorescence emitted (as detected by the pinhole and APD) via laser excitation
is ;4.5 times greater than that of the lamp. Therefore, a fully labeled synapse
excited entirely by the laser would yield ;320 kHz measured by the APD.
Finally, we can compare the DC intensity in our FCS experiment with the
total fluorescence emanating from the synapse. We use laser intensities from
;0.0025 mW to ;0.01 mW. Therefore, if the entire synapse was contained
within the light box of the FCS experiment, the DC intensity would lie
between 160 kHz and 640 kHz. Counting rates in our measurement are 5–70
KHz. This is about an order of magnitude smaller than the synapse’s total
fluorescence and agrees with the ratio of the light box to the synapse size.
APPENDIX C: STICK-AND-DIFFUSE MODEL
In this appendix, we derive the ensemble average subtracted correlation
function for the stick-and-release model. The time average subtracted
correlation function can then be obtained using the results of Appendix D.
In the stick-and-release model, the mobile vesicles are assumed to alternate
between a state in which they are bound to the cytomatrix (stuck) and a second
state in which they are free to diffuse with a diffusion time tD ¼ w2/D, where w
is the width of the laser beam and D is the diffusion constant. They release
with a rate 1/tB when bound and bind with a rate 1/tU when free. Therefore the
vesicles, on average, will be bound for a time tB before freeing and be free for
a time t U before binding. In steady state, the probability that a vesicle is bound
is tB /(tB 1 tU) and free is t U /(tB 1 tU).
The ensemble average subtracted intensity autocorrelation function is
G0 ðtÞ ¼ G0 ð0Þ
Z
t
du Pðu; tÞ
0
1
d=2 ;
ð1 1 u=t D Þ
where d is the dimension and P(u,t) is the probability density that the vesicle
is free for a total time u out of a time interval t $ u. The probability density
P(u,t) can be obtained by summing over the probabilities of having the total
free time u in total time t occurring in n different intervals. This gives
Pðu; tÞ ¼
N
tU
U
U
+ Pn;n ðu; tÞ 1 Pn;n1 ðu; tÞ
t B 1 t U n¼1
N
tB
B
B
+ Pn;n ðu; tÞ 1 Pn1;n ðu; tÞ:
1
t B 1 t U n¼1
Here PUn,m(u,t) is the probability that a vesicle is initially free has total free time
u during the interval t in n free intervals and m bound intervals. PBn,m(u,t) is the
same except the vesicle is initially bound.
Therefore the correlation function Go(t) can be written as an infinite sum.
This sum must be evaluated numerically and can be fairly complicated.
However two limits are readily stated. If the diffusion time tD is long compared
to the free time and sticking time, then the dynamics are essentially the same as
a random walk with a longer time between steps. Therefore the correlation
function will be the same as diffusion with a longer effective diffusion time:
G0 ðtÞ ¼ G0 ð0Þ
FIGURE 11 Fit of FCS data to free diffusion is marginal. The average
correlation function shown in Fig. 2 B is replotted (black line) along with fits
to free diffusion models in one (green line) and two (blue line) dimensions,
with diffusion times of tD ¼ 1.1 and tD ¼ 2.7, respectively. The fit to 2D
free diffusion with 1D confined to twice the light box size (42) is also shown
(red line) and overlies the 1D fit. However, for confined diffusion tD ¼ 2.0,
which is slightly closer to the 2D diffusion constant. All fits were corrected
for finite integration time (Appendix D).
1
d=2 ;
ð1 1 ðt=t D;eff ÞÞ
tD tU ; tB ;
where the effective diffusion time is
t D;eff ¼
tU 1 tB
tD :
tU
In contrast, if the diffusion time is small compared to the other two timescales, the sum in P(u,t) is dominated by the P10 and P01 terms. The correlation function is just the sum of an exponential and diffusion correlation
functions
Biophysical Journal 89(5) 3615–3627
3626
Shtrahman et al.
!
tU
1
tB
t=t
G0 ðtÞ ¼ G0 ð0Þ
1
e B ;
t B 1 t U ð1 1 ðt=t D ÞÞd=2 t B 1 t U
tD tU ; tB :
This is the limit that we observe in our experiments. Note that in this limit,
the correlation function for times t tD is independent of the short time
dynamics and is therefore independent of the dimension d.
APPENDIX D: FCS DATA CORRECTED FOR
FINITE INTEGRATION TIME
The intensity variations measured in most FCS experiments is the correlation
of the deviation of the intensity from the time average intensity. In contrast,
most theoretical analysis concerns the deviation of the intensity from its
ensemble average value. The time average and the ensemble average intensities are the same if the integration time is much larger than the longest
correlation time in the system. However, this is not the case in our experiment.
In this appendix, we derive the relation between the ensemble average
subtracted autocorrelation function and the time average subtracted
autocorrelation function. We introduce the notation Æxæ and x to indicate
the ensemble average and time average, respectively. The ensemble average
subtracted correlation function is then
G0 ðtÞ ¼ ÆDIðt 1 sÞDIðsÞæ;
where DI(t) ¼ I(t) ÆIæ. We assume a steady-state process so that G0(t) is
independent of s. Assuming a total integration time of T, the time average
intensity is
1
I ¼
T
Z
dt IðtÞ:
DIðtÞ ¼ IðtÞ I ¼ IðtÞ ÆIæ ðI ÆIæÞ
¼ DIðtÞ DI;
where DI ¼ I ÆIæ is the difference between the ensemble average and time
average intensity. Therefore the time average subtracted correlation function
GT(t) can be written in terms of the ensemble average subtracted correlation
function as
Z DT
1
GT ðtÞ ¼
dsÆDIðt 1 sÞDIðsÞæ
DT 0
Z DT
1
ds ÆDIðt 1 sÞDIðsÞæ 1 ÆDIDIæ
¼
DT 0
Z DT
2
dsÆDIðsÞDIæ;
DT 0
where DT ¼ T t. The last two terms can be written in terms of the ensemble
subtracted correlation function:
Z
T
s
ds9Go ðs9Þ
ds
0
0
0
DT
dsÆDIðsÞDIæ ¼
1
T
1
We thank Y. Goda and C. Stevens for allowing us to use their data in Fig. 4,
and P. Lau, H. Wang, and X. Zhao for their preparation of the hippocampal
cultures, as well as members of the Bi and Wu labs for their helpful
discussions and comments about the manuscript.
This work was partially supported by the University of Pittsburgh Andrew
Mellon predoctoral fellowship to M.S., National Science Foundation grant
DMR-9986879 to C.Y., Burroughs Wellcome Fund Career Award in the
Biomedical Sciences and National Institutes of Health/National Institutes of
Mental Health grant R01 MH066962 to G.B., and National Aeronautics and
Space Administration grant NAG8-1587, University of Pittsburgh Central
Research Development Fund, and the American Chemical Society
Petroleum Research Fund 36366-AC9 to X.W.
Z
Z
DT
s
ds9Go ðs9Þ
ds
0
1
T
Z
0
Z
DT
ds
0
Biophysical Journal 89(5) 3615–3627
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and
Z
Notice that the time average subtracted correlation function is always
smaller than the ensemble average value. If the integration time is much
larger than the correlation time, the two correction terms are negligible and
GT(t) Go(t). On the other hand, if the correlation time is not much smaller
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shown in Fig. 2 B, the correction is important in our experiments even
though the correlation time is ,1/70th of the integration time.
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0
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2t
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The deviation of the intensity from the time average intensity is
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ÆDIDIæ ¼ 2
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Combining the terms gives the time average subtracted correlation function
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